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Transmitter Point-Ahead using Dual Risley Prisms: Theory and Experiment John Degnan1, Jan McGarry2, Thomas Zagwodzki2, Thomas Varghese3 1Sigma Space Corporation, 2NASA/GSFC, 3Cybioms 16th International Workshop on Laser Ranging Poznan, Poland October 13-17, 2008 Why Transmitter Point-Ahead? Unlike conventional SLR, the eyesafe SLR2000/NGSLR system operates with transmitted pulse energies three orders of magnitude smaller (~60 mJ) and is designed to be autonomous (no operator). Automated pointing of the telescope/receiver is accomplished using a photon-counting quadrant MCP/PMT detector which seeks a uniform distribution of counts among the quadrants. In order to concentrate more laser energy on high satellites, the transmit beam divergence is narrowed by a computer-controlled beam expander in the transmit path. To prevent saturation of the MCP/PMT detector during daylight operations, the receiver FOV must be restricted to roughly + 5 arcsec, which is smaller than the largest anticipated point-ahead angle of 11 arcseconds. Since the transmit and receive FOV’s no longer overlap as in conventional SLR systems, transmitter point ahead (i.e. separate boresighting of the transmitter and receiver) is required. Conventional SLR vs Eyesafe NGSLR Conventional SLR Direct transmitter (green cone) at where target will be one transit time later to maximize signal return. Open up receiver FOV (yellow cone) to capture return signal from previous fire. Minimize false alarms via detection threshold. Eyesafe SLR2000/NGSLR Direct receiver FOV (telescope) to where satellite was one transit time earlier and use Quadrant Detector to correct receiver pointing. Direct transmitter (green cone) at where target will be one transit time later via Dual Risley Prisms to maximize signal return. Reduce receiver FOV (yellow cone) to minimize noise during daylight operations . Transmit and Receive FOV’s no longer overlap. Conventional SLR SLR2000/NGSLR NGSLR Transceiver Block Diagram 0.085 m QUAD Mirror 0.080 m 0.070 m 0.070 m d1 0.130 m 0.250 m Working Distance 0.229 m Star Camera Retro Location 0.350 m d2 Wall 0.105 m 3 X Telescope CCD f = -0.1 m f =0.3 m Telescope 1 2 Pit Mirror Splitter s2' s3 d2 P2 d2 p2 Faraday Isolator/ 0.200 m Half Wave 0.099 m Plate 0 = 67.4o 0.4 m P1 Compensator Block P3 Translation Stage p3 d3 (out of page) 0.051 m NORTH ( = 0o) 0.213 m “Zero” Wedge Day/Night Filters d1 p1 f = 0.108 m 1 d1 5.4X Beam Reducer f2 = -0.02 m p1 3-element Telephoto Lens f=0. 85 m Risley Prisms Special Optics 2x-8x Beam Expander Computercontrolled Diaphragm/ Spatial Filter (Min. Range : 0.5 to 6 mm diameter) d1 p1 Quadrant Ranging Detector 0.04 m f = .025 m Laser Transmitter 0.088 m CCD Camera 0.025 m Vector out of page Vector into page Point-Ahead Procedures Point-ahead angles, expressed in the azimuth and elevation axes of the telescope, are obtained from the orbital prediction program. In determining the appropriate Risley rotation angles, we must properly take into account the complex and time dependent coordinate transformations imposed by the various optical components in the transmit path and the axis rotations of the Coude mount as the pulse travels from the Risleys to the telescope exit aperture. Finally, we must account for any angular biases between the two servo “home” positions and the actual direction of deflection by the prisms. Definition of bAE and Elevation cos Azimuth From Orbital Predictions = azimuth offset between transmit and receive vectors = elevation offset between transmit and receive vectors 2 cos 2 2 tan b AE bAE 2 cos Definition of Coude -Parameter The Coude -Parameter takes into account the axis rotations introduced by the Coude mount and is given by: 0 2 22.5 o where = satellite azimuth = satellite elevation 0 = system specific azimuthal bias = 67.5o for NGSLR Bias Free Risley Command Angles Deflection by an individual prism is in the direction of the thickest part of the wedge. The magnitude of the deflection is given by (n 1) w 15.6arc min where n =1.52 is the refractive index and w = 30 arcmin is the wedge angle The final deflection is the vector sum of the two individual wedge deflections as in the figure. It makes an angle bAE+ with the positive x-axis of the bench. The magnitude is equal to mt where mt is the post-Risley transmitter magnification and is the pointahead angle magnitude. y Desired wedge 2 direction bAE+ Final Beam Direction Projected into bench x-y plane (bAE +) and Magnitude (mt) mt a bAE+ Desired wedge 1 direction a x bAE+ 6a =-(bAE++/2)+/2 =/2-bAE-+/2 5a =bAE+-/2+/2 5a+6a==acos(1-(mt2/22) Physical Explanation First term (/2): Makes the two wedges antiparallel, cancelling out the deflection ( =0), with the individual deflections lying along the bench y-axis. Second term (): Rotates the bench x-y axes into the instantaneous azimuth-elevation (azel) axes at the telescope. Third term (bAE): Rotates the deflection direction to the proper value in the telescope az-el reference system ( still equal to zero). Fourth Term(/2): Provides the final magnitude for , properly accounting for the post-Risley beam magnification, mt , and the wedge deflection angle, . c 5 c 6 2 2 b AE b AE 2 2 mt 2 a cos 1 2 2 Risley Command Angles with Biases The home positions of the servos may be displaced in angle (positive or negative) relative to the bench x-axis leading to “rotational biases” as in the figure. The command angles, 5c and 6c, are therefore adjusted from the actual values, 5a and 6a, according to 5c 5a b1 6c 6a b 2 y Desired wedge 2 direction Stepper Motor 2 “Home” c b2 Final Beam Direction Projected into bench x-y plane (bxy = +5a-6a) and Magnitude (mt) mt Desired wedge 1 direction a bxy a c b1 Stepper Motor 1 “Home” x = satellite point-ahead angle mt = total transmitter magnification beyond Risleys 5a = actual ccw direction of wedge 1 deflection relative to positive bench x-axis 6a =actual cw direction of wedge 2 deflection relative to negative bench x-axis b1 = bias angle between positive bench x-axis and servo 1 home position b2 = bias angle between negative bench x-axis and servo 2 home position 5c = 5a -b1 = commanded direction of wedge 1 deflection 6c = 6a -b2 = commanded direction of wedge 2 deflection bxy = actual angle of deflection relative to positive bench x-axis. Experimental Validation The deflected beam from the Risleys was projected onto the wall and measured for several values of and bAE. The deflected beam was also viewed at the telescope exit window. In a separate set of experiments, a retroreflector placed in the transmit path before the 3-power beam expander reflected the laser beam into the star camera which provided arcsecond quality angular measurements. These experiments were used to: – Check/determine the validity of servo controls and algorithms – Measure the rotational bias angles – Estimate the difference between the two wedge angles. 300 7.5 Experimental Validation at Wall and Telescope Aperture 200 5 100 2.5 0 0 6 6.46.87.27.6 8 8.48.89.29.610 Wall Telescope Aperture 400 15 Bench Y-axis, arcsec 200 0 F F H JJ 100 200 300 400 I 400 300 200 100 0 100 200 300 400 Bench X-axis, arcsec Elevation Axis, arcsec G 300 100 6 6.46.87.27.6 8 8.48.89.29.610 FF 10 5 0 I J 5 i 10 15 G J H 15 10 5 0 5 10 Azimuth Axis, arcsec 10 15 10 10 10 0 These experiments validate the predicted orientation and spread of the spots on the wall and at the telescope aperture. In this particular experiment, was constant at 10 arcsec except for point J ( =0) and bAE took on values 0,90,180, and 270o. As expected, the telescope aperture pattern is rotated by = 90o with respect to the wall pattern and the angular deviations are smaller by a factor mt =28.21. a Star Camera Experiments 320 X0 scale 86.45 300 exp 0.011 Yexp i Ycali b exp 6.905 deg Y0 280 b 1 13.302 deg b 2 6.398 deg Wedge Angle Difference Biases 260 X0 434.333 Y0 278.667 240 380 400 420 440 460 480 Star Camera Origin Xexp i , Xcali •In the above plot, the abscissa and ordinate values correspond to star camera pixel numbers. •Each pixel corresponds to about 0.49 arcsec of movement. •Each individual red square corresponds to the observed location of the retroreflected transmitter spot in the star camera image plane for different point-ahead angles and orientations. •Each blue diamond corresponds to the position predicted by theory. •This experiment provided extremely high angular resolution and provided the numerical values for the rotational biases, b1 and b2. •It also indicated that the wedge angles differed by about 1.1%. Summary The development of the point-ahead algorithms was approached through both theoretical ray analyses and experiment until we achieved agreement. We are now prepared to implement the automated receiver pointing correction and transmitter point-ahead features needed for reliable daylight ranging. During the star camera experimentation, we found that the two prisms have slightly different wedge angles (1.1%) so that zero deflection can never be achieved. Ignoring this difference produces a maximum transmitter pointing error of about 1.5 arcsec for small . For larger , the errors are typically sub-arcsecond. Similar transmitter point-ahead systems and algorithms will be required for future interplanetary laser transponder and communications systems where can take on values of several tens of arcseconds.